The best answer is maybe.
Rising rates are deflationary for the money supply. Historically, with gold backed money, this meant gold price would rise as people needed gold to pay the higher interest. In modern times, however there is no such link. One might argue gold could drop due to people needing to raise liquid capital. But then again, one could argue that gold could rise because the large institutions shorting it would need to close out their positions to recover their collateral.
If interest rates go up every mortgage taken out in London and the South East of England since 2005 is going to go into default. It's not possible for mortgage holders to absorb exponential increases in the cost of lending when wages are at best stagnant and food prices are going up 14.3%.
Many of those mortgages are interest only with no repayment vehicle. The banks will be fucked.